We have shown that a set of tubes with harmonic trapping potentials whose centers are shifted is equivalent to charged particles in a magnetic field in the \(x\) -\(p_y\)  plane.
The underlying idea of our proposal is to replace a momentum in one direction by position to realize a simpler Hamiltonian, which simulates the original Hamiltonian in a hybrid real-momentum space. This method is quite versatile; for example, with a similar mechanism, a collection of one-dimensional Aubry-André model [1]} (the Harper model) with shifted modulation phases simulates a two-dimensional lattice with a magnetic field, the Harper-Hofstadter model [2]}, [3]}, in real-momentum space, without breaking the physical time-reversal symmetry.
Our proposal provides a simple and powerful method applicable to realize various Hamiltonians, opening a possibility for quantum simulation in synthetic quantum matter.
